Consider the signal where α and β are constants. We wish to linearly predict s[...

Consider the signal

where α and β are constants. We wish to linearly predict s[n] from its past p values using the relationship

where the coefficients a_k are constants. The coefficients a_k are chosen to minimize the prediction error

(a) With r_ss [m] denoting the autocorrelation function of s[n], write the equations for the case p = 2 the solution to which will result in a₁, a₂.

(b) Determine a pair of values for α and β such that when p = 2, the solution to the normal equations is a₁ = 11

12 and a₂ = −16 . Is your answer unique? Explain.

(c) If α = 8 and β = −3, determine k-parameter k3, resulting from using the Levinson recursion to solve the normal equations for p = 3. Is that different from k₃ when solving for p = 4?